Consider the space of Bridgeland stability conditions of a suitably nice triangulated category. Autoequivalences of the triangulated category act on the space of stability conditions. Fixing a stability condition imposes extra combinatorial structure on the category, that can be used to study the group of autoequivalences in various different ways. This talk will showcase some of the fascinating structure that emerges via this idea, particularly for 2-Calabi–Yau categories associated to quivers. This is based on joint work with Anand Deopurkar and Anthony M. Licata.